Indecomposability conjecture for domain walls obtained by condensation

Let $\CB$ be a modular tensor category, let $A_1,A_2$ be condensable algebras with

$$\CB_{A_1}^{loc}\simeq\CC_1,\qquad \CB_{A_2}^{loc}\simeq\CC_2,$$

and let $\phi\in\operatorname{Aut}_{\ot}^{\br}(\CB)$.

Domain-wall decomposition conjecture. Any gapped domain wall of the form

$$\CB_{A_1}\boxtimes_{\CB}\phi\boxtimes_{\CB}\CB_{A_2}$$

must be a direct sum of indecomposable gapped domain walls.

The claim is intended to relate condensation from a common phase to decomposition into elementary walls, but the source supplies no proof or resolution.